I’m English (which makes me British. 
)
Some favourite Goon lines:
“Don’t point that moot at me, Moriaty!”
Spike Milligna (the well-known typing error.)
Seagoon:Eccles…overpower the guards.
Eccles:Right. Ill take my boots off.
From The Bridge on the River Wye (with Milligan and Sellers, script by Spike Milligan) :
General Itchikuchi: I have asked you here for a good reason.
Major Barbara: Well I hope I can give you one.
Doc: There is just one question, Sir. How long is this river?
General Itchikuchi: It are 6000 miles.
Barbara: And how wide?
General Itchikuchi: It 300 feet.
Barbara: Then I suggest we build the bridge across it!
Eccles: Ohh!!
Barbara: Is he mad?
Lt. English: He has a certificate, sir.
Barbara: It will mean certain death!
Lt. English: It is a death certificate, sir.
U Bai Dung: We have observed the sentries on the bridge. They cross every ten minutes and uncross ten minutes later.
Hawkins: The double-crossing swines!
I’ve heard it too, though it’s been many years, from the mouths of old people when I was a kid. Right in the middle of the U.S.
I’ve been listening to the Goon Shows fairly regularly for the last year or so (via the iPlayer), and here’s my view:
The audience laughed because it’s a poo joke, but one not so overt as to raise the BBC censor’s dander. And “bound” means “constipated” in this context.
I’ve been listening to Goon Shows for more than 50 years, and I agree.
Not quite so old - written by Sydney Carter.
Concur with the poo joke inference, but as the scene unfolds it turns out to be nothing to do with poop, which is a way of demonstrating the dirty minds of the audience.
With the Goon show, there is also the fairly high chance that there really wasn’t anything all that funny about the line, but something was happening on stage. They were fairly well known for messing around, hence some of the less explicable audience reactions.